Mathematics - Parabola Question with Solution | TestHub

Consider the circle $C:x^2+y^2=4$ and the parabola $P:y^2=8x$. If the set of all values of $\alpha$, for which three chords of the circle $C$ on three distinct lines passing through the point $(\alpha ,0)$ are bisected by the parabola $P$ is the interval $(p,q)$, then $(2q-p{)}^2$ is equal to ________